I think it’s best to get new guitar students playing simple melodies as soon as possible. The song I always seem to go to as “the very first song” is the very familiar “Ode to Joy”.
You can easily pick it out without written music, and it’s good to learn how to “play by ear”. That gives you a feeling for how the strings go together.
But it is good to learn how to read music too. Guitar playing can be so much more than just strumming chords.
Here is “Ode to Joy” in three different keys and played at 6 different positions on the neck. All of these versions are very easy.